Penrose Tile Beading with Garden Weave

I released a new tutorial this month on Garden Weave.

Garden Weave is a flat beaded angle weave like right angle weave (RAW). This tutorial explains the basics technique of beading and designing with Garden Weave and gives detailed instructions for this pair of easy earrings and a pendant.

Here they are in orange. Super fun! Garden weave is a fun way to explore color combinations with nothing more than seed beads and thread.

The tutorial includes many, many different samples of beadwork and charts that explain their structure. Charts for two different repeating patterns are included so you can let your imagination run wild to make bracelets and design other elaborate pieces with Garden Weave, including the chart for this pendant.

For an extra challenge, the tutorial includes charts and a beaded pendant using Penrose tiles, including this one.

After completing the tutorial, I beaded this large patch of a Penrose tiling with Garden Weave using the techniques I explain in the tutorial.

 Here you can see how big it is.

I'm not sure yet what I'll do with it, but here's a detail.

 

And another!

 Thanks for looking!

Truncated Icosidodecahedron in Beads Crater Moon Beaded Bead

Meet Crater Moon.

and Crater Moon in White...

Each Crater Moon is composed of nearly 2700 beads.

The American Mathematical Society recently posted a photo of an amazing structure on their Facebook page with no comment of who made it. They called it a rhombicosidodecahedron (3.4.5.4) because that is the name of the polyhedron in the very inside layer, but Susan Goldstine noticed that the outside layer is actually a truncated icosadodecahedron (4.6.10). This object is a multilayered compound of unusual polyhedra.

With help from Susan, I figured out how to weave it with seed beads and thread. Susan built this model below using Zometool, and wrote, "This is what the structure above each triangular face of the rhombicosadodecahedron looks like. I feel better about not being able to make out what's going on from the original photo. The cavity has a triangle, six trapezoids, three pentagons, and the hexagon at the top." Furthermore, "Above each core pentagon is half an icosidodecahedron (3.5.3.5)."

To bead it, I used an edge-and-cover weave with 3 mm bugle beads for the edge beads and size 11° seed beads for the cover beads. (There's one exception, where I used 11° seed beads for the short edge beads under the squares.) In other words, every n-gon has 2n beads, including n edge beads alternated with n cover beads, all sewn in a loop.

Here you can see how I started to weave the inside layer, showing the edge-and-cover weave for (3.4.5.4), also known as the rhombicosadodecahedron as I mentioned above.

This is a photo from Ivona Suchmannova of Spiral Beading, showing the first layer curled into a ball.

This is the complete first layer of Crater Moon with 6 mm bugle beads and 11º seed beads. This piece will finish a lot larger than the others because the bugle beads are longer.

Here is the start of the second layer on Ivona's bead. She stitched loops of triangles around the pentagons, connected by at the bugle beads.

This shows the start of layer 2 with the longer, 6 mm bugles. You can see the 5 triangles around the pentagons and the 3 trapezoids around the triangles. The short edge of the trapezoids is the aqua 8°. All other beads are 11° and 6 mm.

 

Next, the center front is still just one layer, 

but layer 2 is nearly complete.  Layer 2 

consists of 30 little 3D pentahedrons sitting 

on top of the squares in the first layer. Four 

little walls like a camping tent, the four other 

sides of the pentahedrons include two 

triangles and two trapezoids. The short sides 

of the trapezoids are the one place where 

we use an 11° instead of a bugle bead.

 

 

 

 

 

 

 

These show the second layer finished. The seed beads in the center of the Xs (aqua below, burgundy above) are the tops of the tents, the one place I used seed beads for edge beads.

This is the start of the third layer. It's triangles and pentagons. Here are the pentagons.

And here you can see both pentagons and triangles.

You can add the pentagons and triangle in two steps, or you can stitch them together.
Here you see 3 of the 12 rings done.

Four more to go!

 Here all 12 are done.

In the fourth layer, I finished the space under the 30 squares, adding two trapezoid loops per square.

The fifth and final layer requires adding 720 size 15° seed beads to the outer surface.  Only then does the Crater Moon really hold its shape neatly.

You should make one.

It's just 11°, 15°, Toho 3 mm bugles, and Fireline 6lb.

And a whole lot of stitches.

Here you can see how big it is, just 1.75 inches across or 45 mm.

If you would like to have your very own Crater Moon, you can find the white one in my Etsy shop here: https://www.etsy.com/listing/579082293/

The larger Crater Moon is available here: https://www.etsy.com/listing/582628369/

Thanks for looking.

P.S. If you'd like to try weaving beads, but you think that the Crater Moon is a little beyond your skill set, have a look in my Etsy shop for tons of other tutorials for all skill levels.

Beaded 4D Archemedean Polytope Omnitruncated 120-Cell

I beaded a four-dimensional thing that I don't understand very well.

What I do know is that it's a beaded version of a 4-D Archimedean polytope that goes by many names.

It's made of different polyhedra, in the same kind of way that a polyhedron is made up of different polygons. 

I learned about this structure from a book called, "The Symmetry of Things" by Conway, Burgiel, and Goodman-Strauss. You can see the various names it goes by in this photo, which is a page out of that book. This page is the direct inspiration for this beadwork. More so, it's a recipe for how all of the loops fit together.

As a mathematician, I simply beaded this recipe using beaded angle weave. Each n-gon is a loop of n beads. The arrangement of the loops is the same and the arrangement of the polygons in Conway's illustration.  (However, I left out the thread to stitch the 10-gons because by the time I got to them, the beadwork didn't need or want it.)

Now that it's done, I'm pretty sure what I beaded is called an omnitruncated 120-cell on Wikipedia. Fritz Obermeyer created and gifted this image into the public domain. Isn't it pretty?

This beautiful blue thing has 2640 total polyhedra:
       120 4.6.10
       720 4.4.10
     1200 4.4.6
       600 4.6.6

I didn't bead anywhere near that entire mathematical object, but I did bead a little chunk of it. In fact, I only finished one of the 120 of the (4.6.10). The weird thing about beading this object is you can just keep adding more and more loops and more and more polygons. It feels a lot like beading the infinite skew polyhedron faujasite because they share many of the same shapes connected in the same ways. However, faujasite is an infinite 3D structure, and this is a finite 4D structure. And in this thing, the angles don't work correctly in 3D. To see what I mean, look at all of the distortion in that blue image above. Everything in the center is squished, and everything near the outside is all stretched out. So you couldn't bead the whole thing the way I beaded mine here. But we can bead lots of different chunks of it. I definitely could have kept going. The challenge as an artist is to decide where to stop.

I made this beaded sculpture by weaving glass beads together with a needle and thread. It contains nearly 25 grams of chocolate bronze size 11° seed beads, which is more than a full tube. There are usually around 100 size 11° seed beads per gram; so that's about 2500 beads. I'm pretty sure it's the only one like it. This piece is very tactile and fun to turn in your hands to see all of the different views.

Largest diameter is 6 cm (2 and 3/8 inches). You could put a piece of cord through it and wear it as a large pendant, if you were so inclined. If you would like to have it, you can find it here in my Etsy shop.  Thanks for looking.

Free Pattern for Puffy Heart SRAW and LOVE Letters

So, there's a blog called Bead Love...

It's a blog of inspirations on love and beads, and a group of about 50 of us bead designers are writing it, one post per week for over a year, until we have all had a turn.  

This week, it was my turn to contribute.  So, here.